The equation in the definition can be interpreted as the zero level
set condition for a formal moment map for the action of the group of
gauge transformations, see [1]}, [2]}. The energy of a gauged holomorphic map \((A,u)\)  is given by
\( E(A,u) = {{2}}\int _\Sigma \left(| {\operatorname{d}}_A u |^2 + |F_A|^2 + |u^*P(\Phi )|^2 \right)  \operatorname{Vol}_\Sigma .\) 
